An Explicit Computation of the Blanchfield Pairing for Arbitrary Links

Abstract

AbstractGiven a linkL, the Blanchfield pairing Bl(L) is a pairing that is defined on the torsion submodule of the Alexander module ofL. In some particular cases, namely ifLis a boundary link or if the Alexander module ofLis torsion, Bl(L) can be computed explicitly; however no formula is known in general. In this article, we compute the Blanchfield pairing of any link, generalizing the aforementioned results. As a corollary, we obtain a new proof that the Blanchûeld pairing is Hermitian. Finally, we also obtain short proofs of several properties of Bl(L).